# Why protons and neutrons have spins?

1. Apr 7, 2005

### Winga

Their spin quantum numbers are 1/2 and -1/2.

How to explain these in terms of quarks?

2. Apr 7, 2005

### marlon

Because they are made of two up quarks and one down quark (uud), protons are baryons. So are neutrons (udd). The magnitude of the spin-value of each quark is 1/2

marlon

3. Apr 7, 2005

### dextercioby

Composing 3 spins of 1/2,according to Clebsch-Gordan's theorem,doesn't necessarily yield a spin 1/2 state...In fact,it yields a linear combination of 1/2 & 3/2 states.Something more is needed to explain the spin of those 2 barions.

Daniel.

4. Apr 7, 2005

### marlon

Angular momentum doesn't add linearly. That is, a proton contains three quarks, but its spin is not 3/2, but 1/2. When you add angular momentum, you have a range of possible results, which goes from the maximum (the arithmetic sum) down to the minimum (the larger minus the smaller) with possible values at unit steps in between. If you add two spin-1/2 fermions, you get either spin 0 or spin 1 (a boson). If you add 5 units of angular momentum to 2 units, you get 3, 4, 5, 6, or 7 units of angular momentum. If you add 3/2 units and 2 units, you get 1/2, 3/2, 5/2, or 7/2 units. A proton has spin 1/2. As you should expect, there's another particle with the same quark content as the proton, but spin 3/2, the Δ+.

marlon

5. Apr 7, 2005

### Winga

Are quarks also have spins, +1/2 & -1/2?

6. Apr 7, 2005

### dextercioby

Eigenvalues of $$\hat{S}_{z}$$...?Of course.

Daniel.

7. Apr 8, 2005

### humanino

Let me just say that the truth is far more complex than the simple constituent quark model could let one think

see for instance : Present understanding of the nucleon spin structure

there are several contribution to the spin of the nucleon, and it is a superbe illustration of the strength of QFT that they precisely add up to exactly one-half. The experimetal resolution of this puzzle is currently being performed.

8. Apr 8, 2005

### Winga

Is there any easier way to explain this phenomenon?

9. Apr 8, 2005

### marlon

No, sorry, this is QM. Though the explanation by Humanino is entirely correct, i suggest you make sure you understand how addition of the J-operator and the associated Clebsch-Gordan coefficients work. This is basic QM-stuff.

Question is : did you study any QM yet ?

regards
marlon

10. Apr 8, 2005

### Winga

Mmmm...not yet!

11. Apr 8, 2005

### marlon

In that case, Houston we have a problem...

Within what context do you need to answer this question of proton-spin ?

regards
marlon

12. Apr 8, 2005

### dextercioby

No offense,but "Their spin quantum numbers are 1/2 and -1/2.

How to explain these in terms of quarks?" and "Not yet" when asked about studying QM,do not really match.There's an order to everything...You can ask about everything,it's a forum,but the explanations you asked for "...in terms of quarks" are not simple to understand,if you have no theoretical preparation...

Daniel.

13. Apr 8, 2005

### Staff: Mentor

14. Apr 8, 2005

### marlon

The first site given by astronuc indeed gives a splendid explanation as to why there are six quarks. However, it does not explain the problem at hand here. one cannot bypass the QM-nature of it's solution.

regards
marlon

15. Apr 10, 2005

### Winga

For protons, the spin of one up quark cancels out the spin of one down quark, and one up quark left with spin value 1/2?

16. Apr 10, 2005

### Haelfix

Unfortunately its not that simple. Spins don't add like regular numbers in quantum mechanics much less field theory. You have to play an intricate game with things called Clebsch Gordon Coefficients and the like. A first course in QM should suffice to explain the correct algebra.

17. Apr 10, 2005

### Mk

Would the correct algebra be able to be taught here? If not, where can I find an easy explination of what to do?

18. Apr 10, 2005

### NEOclassic

The CRC Handbook for 2002 says:

Hi Winga,
The free neutron undergoes, with half-life of 614 seconds, a convulsive transformation to a proton + a 782 KeV beta- and its spin is +1/2 and its magnetic dipole moment is -1.913 nuclear magneton units.
The residual Proton's spin is also +1/2 but its magnetic dipole moment is
+2.793 nuclear magniton units. Cheers, Jim